I got sick with chronic sinus drainage, pain, etc., and both teeth eventually had to be pulled.
The first time, the infection/illness cleared up immediately, within 24 hours after the tooth was pulled. Before that I'd even undergone sinus surgery trying to fix what was thought to be a sinus problem only.
The second time, the dentist punctured up into the sinus and I've had low-grade drainage that's remained ever since, 2 years ago, despite lots of expensive tests and trips to a half dozen different experts, both medical and dental.
I would not have another root canal as my teeth apparently have lots more roots than usual, and even with a microscopic tool the second time, a root was still missed.
A dental infection can go to your heart or other organs via the bloodstream, FYI.
If you've had one and feel fine, I would not worry about it. But if you're ill over a long time on the side the tooth is on, get it checked out. Mine were both redone twice, and still they didn't find all the problems.